n^2+18n+16=0

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Solution for n^2+18n+16=0 equation: 


Simplifying
n2 + 18n + 16 = 0

Reorder the terms:
16 + 18n + n2 = 0

Solving
16 + 18n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 18n + -16 + n2 = 0 + -16

Reorder the terms:
16 + -16 + 18n + n2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 18n + n2 = 0 + -16
18n + n2 = 0 + -16

Combine like terms: 0 + -16 = -16
18n + n2 = -16

The n term is 18n.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18n + 81 + n2 = -16 + 81

Reorder the terms:
81 + 18n + n2 = -16 + 81

Combine like terms: -16 + 81 = 65
81 + 18n + n2 = 65

Factor a perfect square on the left side:
(n + 9)(n + 9) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(n + 9) equal to 8.062257748 and -8.062257748.


Subproblem 1
n + 9 = 8.062257748

Simplifying
n + 9 = 8.062257748

Reorder the terms:
9 + n = 8.062257748

Solving
9 + n = 8.062257748

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + n = 8.062257748 + -9

Combine like terms: 9 + -9 = 0
0 + n = 8.062257748 + -9
n = 8.062257748 + -9

Combine like terms: 8.062257748 + -9 = -0.937742252
n = -0.937742252

Simplifying
n = -0.937742252


Subproblem 2
n + 9 = -8.062257748

Simplifying
n + 9 = -8.062257748

Reorder the terms:
9 + n = -8.062257748

Solving
9 + n = -8.062257748

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + n = -8.062257748 + -9

Combine like terms: 9 + -9 = 0
0 + n = -8.062257748 + -9
n = -8.062257748 + -9

Combine like terms: -8.062257748 + -9 = -17.062257748
n = -17.062257748

Simplifying
n = -17.062257748


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.937742252, -17.062257748}

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